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Cramer-Rao lower bounds for inverse scattering problems of multilayer structures

Gustafsson, Mats LU orcid and Nordebo, Sven LU (2006) In Inverse Problems 22(4). p.1359-1380
Abstract
In this paper, the inverse scattering problem of amultilayer structure is analysed with the Fisher information matrix and the Cramer-Rao lower bound (CRLB). The CRLB quantifies the ill-posedness of the inverse scattering problem in terms of resolution versus estimation accuracy based on the observation of noisy data. The limit for feasible inversion is identified by an asymptotic eigenvalue analysis of the Toeplitz Fisher information matrix and an application of the sampling theorem. It is shown that the resolution is inversely proportional to the bandwidth of the reflection data and that the CRLB increases linearly with the number of slabs. The transmission data give a rank-1 Fisher information matrix which can approximately reduce the... (More)
In this paper, the inverse scattering problem of amultilayer structure is analysed with the Fisher information matrix and the Cramer-Rao lower bound (CRLB). The CRLB quantifies the ill-posedness of the inverse scattering problem in terms of resolution versus estimation accuracy based on the observation of noisy data. The limit for feasible inversion is identified by an asymptotic eigenvalue analysis of the Toeplitz Fisher information matrix and an application of the sampling theorem. It is shown that the resolution is inversely proportional to the bandwidth of the reflection data and that the CRLB increases linearly with the number of slabs. The transmission data give a rank-1 Fisher information matrix which can approximately reduce the CRLB by a factor of 4. Moreover, the effect of dispersive material parameters and simultaneous estimation of two material parameters are analysed. The results are illustrated with numerical examples. (Less)
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Inverse Problems
volume
22
issue
4
pages
1359 - 1380
publisher
IOP Publishing
external identifiers
  • wos:000239164600015
  • scopus:33746295326
ISSN
0266-5611
DOI
10.1088/0266-5611/22/4/014
language
English
LU publication?
yes
id
99aefa4e-8f29-414d-b87c-be6cf824b83d (old id 401364)
date added to LUP
2016-04-01 11:45:14
date last changed
2021-03-31 03:53:03
@article{99aefa4e-8f29-414d-b87c-be6cf824b83d,
  abstract     = {In this paper, the inverse scattering problem of amultilayer structure is analysed with the Fisher information matrix and the Cramer-Rao lower bound (CRLB). The CRLB quantifies the ill-posedness of the inverse scattering problem in terms of resolution versus estimation accuracy based on the observation of noisy data. The limit for feasible inversion is identified by an asymptotic eigenvalue analysis of the Toeplitz Fisher information matrix and an application of the sampling theorem. It is shown that the resolution is inversely proportional to the bandwidth of the reflection data and that the CRLB increases linearly with the number of slabs. The transmission data give a rank-1 Fisher information matrix which can approximately reduce the CRLB by a factor of 4. Moreover, the effect of dispersive material parameters and simultaneous estimation of two material parameters are analysed. The results are illustrated with numerical examples.},
  author       = {Gustafsson, Mats and Nordebo, Sven},
  issn         = {0266-5611},
  language     = {eng},
  number       = {4},
  pages        = {1359--1380},
  publisher    = {IOP Publishing},
  series       = {Inverse Problems},
  title        = {Cramer-Rao lower bounds for inverse scattering problems of multilayer structures},
  url          = {http://dx.doi.org/10.1088/0266-5611/22/4/014},
  doi          = {10.1088/0266-5611/22/4/014},
  volume       = {22},
  year         = {2006},
}